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Tuesday, March 25, 2014

From 1992 - David Klein and Jerry Rosen on fuzzy math and why we have it

The 1992 Mathematics Framework for California Public Schools governs, to a considerable extent, the mathematics curriculum in California's public schools. It is a model of mediocrity. The Framework recommends that calculators be issued to kindergartners and used in all K-12 grades; it strongly discourages placing students by ability or achievement; it advocates that teachers do more "facilitating" and less "teaching;" it discourages testing, and promotes portfolios, "authentic assessment," and "holistic scoring rubrics;" it de-emphasizes basic skills and promotes "cooperative work" over individual responsibility. In short, it is the bible of "fuzzy math."

[snip]

Why is this kind of mediocrity promoted by so many education professors and education experts? We suggest that it is simply good intentions gone awry, resulting in institutionalized "liberal racism." Liberal education experts fear that minority students can't learn real math because of "cultural differences." They recognize that it would be preposterous to lower standards only for those students while maintaining high standards for other groups. Thus, the education experts lower standards for everyone, with "authentic assessment" replacing hard-core, standardized tests, and so-called "higher order thinking" supplanting basic skills.

The clearest refutation of the racism disguised by the Framework comes from the work of Jaime Escalante, the teacher who was immortalized in the movie, "Stand and Deliver." Mr. Escalante proved beyond any doubt that minority students from poor neighborhoods can do as well in mathematics as any other group. His methods were traditional and "non fuzzy."

But today, as a classroom instructor teaching "basic" composition, I wonder.

I've mentioned this before, but it bears repeating: college freshmen whose skills are far below where they need to be can be perfectly intelligent and 'smart' when you stick to spoken language.

They can be and they are.

In fact, it's not necessarily possible to tell which students have better skills and which poorer by listening to classroom discussion.

The Cambridge Pre-U courses are a case in point. I gather Cambridge Pre-U is being sold to districts (and to parents) as a rigorous replacement for AP courses that does not require grouping. All kids, at all levels of skill and ability, can take the same course and it's still advanced.

The reason that claim can be made is that the courses -- at least the one I witnessed -- primarily involve Googling (there is no assigned reading), creating group Powerpoints for presentation to the class, and class discussion. (The class I saw required one paper, written at the end of a year and a half of 'study.')

Afterwards, the principal told us how wonderful the class is because you can't tell the AP kids apart from the non-AP kids.

Then he said proudly that the student who had done all the challenging was a kid who would never have been allowed to take a regular AP course in his school.

Naturally, that got my dander up. A talented student who hadn't been prepared by his school to take an AP course didn't seem like something a principal should be talking about with anything other than embarrassment and regret.

Today I feel a bit differently.

I certainly believe that the student I saw in action should have been prepared by his school to take one Advanced Placement course by graduation. He was headed for college, and that being the case, preparing him for AP was the school's job.

On the other hand, I now know that being smart and capable in speech does not mean being smart and capable in writing. Not even close.

I also know that writing really is thinking in any number of ways. Which means if you can't write....you're not the smartest person in the room.

So, back to Klein and Rosen. It now seems entirely plausible to me that, like me, a large contingent of education reformers has registered the fact that that underprivileged students fare better talking than writing (or doing math).

Education reformers don't have to have decided consciously to tackle the achievement gap by making math into a discussion subject in order to have done just that.

10 comments:

Froggiemama
said...

"college freshmen whose skills are far below where they need to be can be perfectly intelligent and 'smart' when you stick to spoken language."

Really? I don't see that at all with my college kids. I also get a lot of very underprepared kids, and I find almost universally that the ones who speak well are the ones who write well and who are good at the computer science assignments I give them. The ones who have trouble are also extremely inarticulate. I suspect that the problem is that they don't have enough vocabulary to read their textbook or to follow the discussion in class. They also exhibit very imprecise thinking habits, which is a big problem when you are trying to write programs. No, I do not see students who are bad at writing but good speakers, not at all.

If schools are not explicitly teaching and requiring mastery of the appropriate grade-level content, across all subjects, before advancement, most of the kids who will be ready for real HS college-prep work (let alone honors or AP) will be those at the top end of the ability curve, who are also the most likely to be the most advantaged and the most likely to have received significant instruction outside of school (parents, online, CC, Kumon etc) - cue Steve H on that.

Schools refuse to see that their failure to group by instructional need/level, by subject, disproportionately hurts those who depend on schools for all of their academic knowledge and skills. Advantaged kids have parents who know what kids should be learning and who will supplement as necessary; math facts, std algorithms, vocab, good lit and non-fiction, composition, grammar, history, art/music history, science - all those things schools now expect kids to "discover" - which they don't. They arrive in 7th-9th behind the 8-ball and likely to stay there.

But knowing how to see a flaw is different than successfully constructing an argument.

We blog commenters have mastered tis fact!

Seeing a hole in an argument doesn't mean you can think through a thesis topic succinctly, nor cite supporting evidence.

To the bigger point, it is not that schools refuse to see how they are hurting kids, it is that individuals in those schools have weighed that against the cost of being called racist or classist and decided not to bother.

I think educators long ago believed they could level the playing field by moving away from the quantitative skills and analytic needs of math and sci courses, yes. Same reason they make movies, songs and dioramas instead of book reports, too.

"Mr. Escalante proved beyond any doubt that minority students from poor neighborhoods can do as well in mathematics as any other group."

to dance close to the third rail,

But he didn't show that the amount of time and effort needed for them to do well was the same as for any other group. and that is what schools do when they mix-group -- everyone has the same amount of time. and iy isn't enough.

"Schools refuse to see that their failure to group by instructional need/level, by subject, disproportionately hurts those who depend on schools for all of their academic knowledge and skills."

Yes. We parents have gotten numerous notes telling us to practice math facts at home. It's amazing that the implication of this doesn't sink in to them.

Barry and I talk about this hidden tracking in schools. Many educators assume that if they don't track, then all kids have equal opportunity and help. I think that's where many IQ arguments come from. If my son was an average student, my help at home would have made an even bigger difference. An older teacher once told me that it's the middle students who get hurt the most. Bright students in my son's fifth grade still had not mastered the times table. That was shocking to some, but if it happens in an urban school, well, maybe there's something else going on. Never mind that the failure was clearly shown for the school in the affluent area.

I think Catherine is right about the difference between fluent, intelligent speech and being able to read or write.

A mentor warned my husband was warned about this phenomenon when he was a graduate student TA-ing at a college with weak undergraduates. The mentor said that while the students could be very strong in classroom discussion, they couldn't understand the class reading and they couldn't write well. That was 15+ years ago.

Like Froggiemama, I have not observed students who write poorly but come across as sharp when speaking. It may be because we are both dealing with highly technical subjects where attention to detail is essential. Students who are vague and disorganized in their writing are also vague and disorganized in their verbal presentations. It is a lot harder to BS your way through a technical discussion than a current events discussion.

I've seen very high correlation between technical skills (programming and problem solving) and writing skills—except for one big problem: writers' block. I know several highly competent (even brilliant) people who failed to get their PhDs because they could not write their thesis, even though they had done all the research, and were capable of writing well when the stakes were lower.